Why do we differentiate a function if we can draw its graph and identify the minimum? Is the only reason that functions could get very complicated to plot but easier to differentiate (which I guess would be a big reason)?
2026-05-13 18:29:31.1778696971
Find minimum value: Drawing a graph vs differentiation?
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Even if we differentiate just to get the minimum, sometime differentiation is much faster than plotting. Suppose you have a family of simple quadratics, $ax^2+bx+c$ with each of $a,b,c$ taking hundreds of values. Can you find the minimum?
Secondly, taking derivatives also has different use. It is the tangent to a curve. Minimum and maximum are only if this value is $0$. Also, in physics, the derivative can have a special meaning. Derivative of position with respect to time is the velocity. The derivative of velocity with respect to time it's called acceleration.
Thirdly, differentiation is a "simple" step in further, more advanced mathematics, such as integrals and differential equations.