You are given $$\mathrm{f}(x)=x^2,\qquad \mathrm{f}'(x)=2x.$$ Complete the table. $x$Height \(\mat

Question

You are given $$\mathrm{f}(x)=x^2,\qquad \mathrm{f}'(x)=2x.$$ Complete the table. $x$Height $\mathrm{f}(x)$Gradient $\mathrm{f}'(x)$ $-2$ $0$ $2$ Explain why the points at $x=-2$ and $x=2$ have the same height but different gradients. At which of these three points is the tangent horizontal?

Accepted Answer

(a) Heights $4,0,4$; gradients $-4,0,4$; (b) Equal heights but opposite slopes; (c) Horizontal at $(0,0)$.

\(x\)	Height \(\mathrm{f}(x)\)	Gradient \(\mathrm{f}'(x)\)
\(-2\)
\(0\)
\(2\)

Differentiation

Differentiation

Solution:

Solution locked