Question

Help on calculus! Semi circle!

Answer 1

A. f(t)'s domain is from 0 to 6, and h(x) is an integral of t(x) from 0 to 2x-1. So, 2x-1 has to between 0 and 6. Simplify the inequality:
0 < 2x-1 < 6

Answer 2

UON: What do YOU think is the domain of this function, and why?

Answer 3

0 = 2x - 1
x = ½

6 = 2x - 1
x= 3.5

For domain, yes? No?

Answer 4

Yes, as far as I can tell.

For B, the derivative of a definite integral is just the original function evaluated at the limits of integration. If x = 2.5, what is f(2x-1)?

Answer 5

For C, is there a point where the sum of areas under the curve start decreasing? (i.e. where the function dips below the x axis?)

Answer 6

B. 2((2.5)-1) = 4

C. it dips below the x-axis on four

Answer 7

Yup. So, can you explain why x = 4 is a maximum of h(x)

Answer 8

Wai sec, my niece is crying. Im on baby duty lol.

Answer 9

Yes. Though I guess the maximum is at x = 2.5, not 4. My bad.

Answer 10

Okay, thanks for your help! :D