given : g(6)=3 and g prime(6)=-4 B)let p(x)=x^4/g(x),find p prime (6)

Question

step by step and explanation of steps ,thanks.

Answer 1

given : g(6)=3 and g prime(6)=-4 B)let p(x)=x^4/g(x),find p prime (6)

This is just the use of the quotient rule in calculus.

If y(x) = u(x)*v(x), then,

y’(x) = (v*u’ – v’*u) / v^2

Taking p(x) = h(x) / g(x), where h(x) = x^4 and h’(x) = 4x^3, then

p’(x) = (g*h’ – g’*h) / g^2

p’(6) = (g(6)*h’(6) – g’(6)*h(6)) / g(6)^2

using g(6) = 3, h’(6) = 4*6^3, g’(6) = -4, h(6) = 6^4, then

p’(6) = (3*4*6^3 – (-4)*6^4) / 3^2

p’(6) = 6^3*(12 + 24) / 9

p’(6) = 216*36/9 = 864

Answer: p’(6) = 864