# Question #36745

Jul 28, 2016

Slope is 4.

#### Explanation:

The gradient or slope of the tangent to the curve at a point is given by evaluating the first derivative of the function at that point.

For $f \left(x\right) = 2 {x}^{2} + 1$ we shall compute the derivative using the power rule:

For $y = {x}^{n} \rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = n {x}^{n - 1}$

So $f ' \left(x\right) = 2 \left(2 {x}^{1}\right) + 0 = 4 x$

Slope given by $f ' \left(1\right) = 4 \left(1\right) = 4$