Answer:
y - 7 = 4(x - 35)
Step-by-step explanation:
The fundamental theorem of calculus states that:
[tex]\frac{d}{dx}[/tex] [tex]\int\limits^x_a {f(t)} \, dt[/tex] = 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)
