SOLUTION: Suppose F(x) = f(g(x)) where f(-2)=8 f'(-2)=4 f'(5)=3 g(5)=-2 g'(5)=6 Find F'(5)

Algebra.Com
Question 1203886: Suppose F(x) = f(g(x)) where
f(-2)=8
f'(-2)=4
f'(5)=3
g(5)=-2
g'(5)=6
Find F'(5)

Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Answer: 24

Work Shown

F(x) = f(g(x))
F ' (x) = f ' (g(x)) * g ' (x) ...... chain rule
F ' (5) = f ' (g(5)) * g ' (5)
F ' (5) = f ' (-2) * 6
F ' (5) = 4 * 6
F ' (5) = 24

The relevant given info was
f'(-2)=4
g(5)=-2
g'(5)=6

While the following info wasn't needed
f(-2)=8
f'(5)=3
This likely was designed by your teacher to throw off the student (as a trick answer of sorts)

RELATED QUESTIONS

Let f(x)=3x^2-7x+5 and g(x)=x^2+4. Find f+g,f-g,f*g, and f/g. Simplify your answers.... (answered by MathLover1)
f(x)=2x²-2x-12 and g{x}=3 find: 1. f(2) 2. g(-2) 3. f(-3) 4. f(-1) 5. (f+g)x 6.... (answered by MathLover1)
f(5)+g(-2)= (answered by EMStelley)
f(x)=x^2 + 3 and g(x) = -2x + 6 Find (fg)(4) Find (f+g)(3) Find (f/g)(5) Find... (answered by Tatiana_Stebko)
given f(x)=-3x^2+x and g(x)=5, find f+g, f-g, fg, and... (answered by josgarithmetic)
Use the functions f(x) = 2x +7, g(x) = x squared + 3x, and h(x) = 1/x-7 to find each of... (answered by funmath)
find the value if f(x)=5/x+2 and g(x)=-2x+3 1.)f(-4) 2.)g(1/2 3.)g(-6)... (answered by math_helper,MathTherapy,ikleyn)
f(x)=x+5 g(x)=x^2-4x+5 h(x)=3x^2-2x+5 find (f+g)(x) find (f*h)(x) find f[g(2)] (answered by solver91311)
find f [g(6)] and g [f(6)]. f(x)=2x-1; g(x)=x^2+5 (answered by oscargut)