# I need help on an AP Calculus problem!!!!?

This is the exact question as it is written in the booklet.
TABLE
x f(x) f '(x) g(x) g'(x)
1 6 4 2 5
2 9 2 3 1
3 10 -4 4 2
4 -1 3 6 7
The function f and g are differentiable for all real numbers, and g is strictly increasing. The table gives values of the functions and their first derivatives at...
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This is the exact question as it is written in the booklet.

TABLE

x f(x) f '(x) g(x) g'(x)

1 6 4 2 5

2 9 2 3 1

3 10 -4 4 2

4 -1 3 6 7

The function f and g are differentiable for all real numbers, and g is strictly increasing. The table gives values of the functions and their first derivatives at selected values of x. The function h(x) = f(g(x)) - 6.

(a) Explain why there must be a value r for 1<r<3 such that h(r) = -5

(b) Explain why there must be a value c for 1<c<3 such that h'(c) = -5

(c) Estimate f ''(2.5)

(d) If g^-1 is the inverse function of g, write the equation of the line tangent to the graph of y = the inverse of g^(x) at x=2

TABLE

x f(x) f '(x) g(x) g'(x)

1 6 4 2 5

2 9 2 3 1

3 10 -4 4 2

4 -1 3 6 7

The function f and g are differentiable for all real numbers, and g is strictly increasing. The table gives values of the functions and their first derivatives at selected values of x. The function h(x) = f(g(x)) - 6.

(a) Explain why there must be a value r for 1<r<3 such that h(r) = -5

(b) Explain why there must be a value c for 1<c<3 such that h'(c) = -5

(c) Estimate f ''(2.5)

(d) If g^-1 is the inverse function of g, write the equation of the line tangent to the graph of y = the inverse of g^(x) at x=2

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