Two curves are $$ \mathrm{f}(x)=x^2-4x+1, \qquad \mathrm{g}(x)=x^2-4x+7.$$ Find $\mathrm{f}'(x)$ a

Question

Two curves are $$ \mathrm{f}(x)=x^2-4x+1, \qquad \mathrm{g}(x)=x^2-4x+7.$$ Find $\mathrm{f}'(x)$ and $\mathrm{g}'(x)$. Find the point on each curve where the tangent is horizontal. Explain why the gradient functions are equal even though the points in part (b) are different.

Accepted Answer

(a) $\mathrm{f}'=\mathrm{g}'=2x-4$; (b) Points $(2,-3)$, $(2,3)$; (c) The curves differ by a vertical shift of $6$.

Differentiation

Differentiation

Solution:

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