let $f(x)=x^4 + \sin x$
Show that there exists $x \in (-2,2)$ such that $f'(x) = 0$.
2026-02-23 00:28:59.1771806539
Showing point in f(x) such that f'(x)=0 exists
45 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
2
There are 2 best solutions below
Related Questions in REAL-ANALYSIS
- how is my proof on equinumerous sets
- Finding radius of convergence $\sum _{n=0}^{}(2+(-1)^n)^nz^n$
- Optimization - If the sum of objective functions are similar, will sum of argmax's be similar
- On sufficient condition for pre-compactness "in measure"(i.e. in Young measure space)
- Justify an approximation of $\sum_{n=1}^\infty G_n/\binom{\frac{n}{2}+\frac{1}{2}}{\frac{n}{2}}$, where $G_n$ denotes the Gregory coefficients
- Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$
- Is this relating to continuous functions conjecture correct?
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Absolutely continuous functions are dense in $L^1$
- A particular exercise on convergence of recursive sequence
Related Questions in DERIVATIVES
- Derivative of $ \sqrt x + sinx $
- Second directional derivative of a scaler in polar coordinate
- A problem on mathematical analysis.
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Does there exist any relationship between non-constant $N$-Exhaustible function and differentiability?
- Holding intermediate variables constant in partial derivative chain rule
- How would I simplify this fraction easily?
- Why is the derivative of a vector in polar form the cross product?
- Proving smoothness for a sequence of functions.
- Gradient and Hessian of quadratic form
Related Questions in ROLLES-THEOREM
- Find the differential function $f$ satisfies the following conditions
- Proof of polynomial expression by Rolle's theorem
- Confirmation of Proof: $f(x)= x^5 - x - 16$ has at most three real roots.
- Number of real roots of a quintic polynomial
- Number of distinct real roots of derivative of a function
- Determine all $x \in \mathbb{R}$ so that $2^x = x^2+1$
- Prove that a degree-$6$ polynomial has exactly $2$ real roots
- Rolles theorem word problem - find the c - double checking my answer
- The equation $x^3-6x^2-5x+12=0$ has at least one root between :-
- Proving a polynomial has x amount of zeros
Related Questions in STATIONARY-POINT
- Stationary Condition of Variational Iteration Method
- Finding the largest area of a right-angled triangle using Lagrange multipliers
- Why is a stationary point of a curve given by parametric equations on a surface not a stationary point of the function itself?
- Convergence concerning the $\alpha$th derivative of $f(x)=x^\alpha-\alpha^x$
- Number of equilibrium points, first order ODE
- Finding stationary points of a function when substitution method fails
- Bifurcation, critical points and parameter dependence in $\nabla_r\,\phi_a(r) = 0$ when varying $a$
- What does equation of error function to zero exactly do?
- Proving that a function in $\mathbb{R^3}$ has a minimum on a set
- Why is $2$ double root of the derivative?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Hint: $f(\frac{\pi}{2}), f(-\frac{\pi}{2})> 0$, $f(0)=0$.