Find (f^1)'(a). f(x)=3x^3+4x^2+4x+2, a=2

Question

A) Find (f^1)'(a). f(x)=3x^3+4x^2+4x+2, a=2

B) A cylinder is being flattened so that its volume does not change. Find the rate of change of radius when r=3 inches and h=5 inches, if the height is decreasing at 0.2 in/sec. Hint: what is the rate of change of volume?

Answer 1

A) f(x) = 2; 3x³ + 4x² + 4x + 2 = 2; x = x = 0; 3x² + 4x + 4 = 0 (no real solutions); f^-1(2) = 0; f'(x) = 9x² + 8x + 4

So, (f^-1)'(2) = 1/f'(0) = 1/4

B)V = πr²h; dV/dt = 0 = π(2rhdr/dt + r²dh/dt); dr/dt = - (rdh/dt)/(2h) = - (- 0.2in/s·3in)/(10in) = 0.06 in/s