Question

Can anyone solve part C?​

Answer 1

It going to be y- 7= 4 (x-35)

Answer 2

Answer:

y - 7 = 4(x - 35)

Step-by-step explanation:

The fundamental theorem of calculus states that:

$\frac{d}{dx}$ $\int\limits^x_a {f(t)} \, dt$ = f(x).

So using the fundamental theorem of calculus, you can find that h'(x) = f(x).

The question tells you that f(x) is periodic with a period of 8, so f(x) repeats itself every 8 units.

Using this, you can find that the slope of h(x) at x = 35 is the same as the slope of h(x) at x = 3, which is 4.

The slope of h(x) at x = 35 is 4.

Now I have to find the value of h(x) when x = 35. It is the area under f(x) from 0 to 35.

The area underneath f(x) from 0 to 35 is 7. When x = 35, h(x) = 7.

Now use the point-slope formula to write the equation of the tangent line.

The answer is y - 7 = 4(x - 35)