Question

If f(x) = 8sin(x2)+4, where x is measured in radians, then what is the slope of f(x) at x = 2?

Answer 1

Answer:

Slope $\frac{dy}{dx} =16cos(4)$

Step-by-step explanation:

Since it is given that

$f(x)=8sin(2x)+4$......................(1)

Where x is in radians

Now for finding the slope we need to derivate the equation (1) with repect to $x$ as f is a function of $x$.

so, differentiate equation (1)

$f'(x)^{}=8cos(2x)\times2+0\\f'(x)=16cos(2x)$..............(2)

we need to find the slope at $x=2$

so, put $x=2$ in equation (2)

$f'(x)=16cos(2\times2)\\f'(x)=16cos(4)$

So, slope $\frac{dy}{dx} =16cos(4)$