The functions f and g are differentiable for all real numbers x. the table below gives values for the functions and their first derivatives at selected values of x.
x f(x) f'(x) g(x) g'(x)
1 4 -3 5 2
2 -3 -1 4 6
3 π 8 -1 4
4 -5 unknown 0 3
a. if the function h is given by h(x) = f (x) / g(x)' find h'(1).
b. if the function r is given by r(x) = f (x)g(x), find the equation of the tangent line to r(x) at x = 2.

13/9

y =-22x+32

Step-by-step explanation:

Given that the functions f and g are differentiable for all real numbers x. The table below gives values for the functions and their first derivatives at selected values of x.

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

1 4 -3 5 2

2 -3 -1 4 6

3 π 8 -1 4

4 -5 unknown 0 3

a)

(using quotient rule)

Substitute 1 for x

b)

when

point of contact is (2,-12)

Slope of tangent =

Using point slope form, tangent is

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3

d.) yes, because the volume of the cone is greater than the volume of the sphere

step-by-step explanation: