Let's say there is a tangent: $y=3x^2+4x-5$
The given point is: $(1,2)$
And we need to find the gradient.
Should I sub $1$ and $2$ into $x$ and $y$ or should I use the quadratic function?
2026-03-25 19:10:39.1774465839
Sub it in or use another way?
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This thing is changing faster than I can type! If the curve is given by $y= 3x^2+ 4x- 5$ then, since $y= 3(1^2)+ 4(1)- 5= 3+ 4- 5= 2$, yes, (1, 2) is on that curve. The derivative is $y'= 6x+ 4$. At x= 1 the gradient of the curve is $y'= 6(1)+ 4= 10$. The tangent line to the curve at x= 1 is y= 10x- 8.