For $y=x^2+1$, a student wants the gradient at $x=3$. The student writes: \[y=3^2+1=10, \qq

Question

For $y=x^2+1$, a student wants the gradient at $x=3$. The student writes: $$y=3^2+1=10, \qquad \frac{\mathrm{d}y}{\mathrm{d}x}=0 \quad\text{because $10$ is constant.}$$ Explain the error. Find the correct gradient at $x=3$. Find the coordinates of the point.

Accepted Answer

(a) Differentiate before substituting; (b) Gradient $6$; (c) Point $(3,10)$.

Differentiation

Differentiation

Solution:

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