Question

Let f(x) = x⁵ + 2x – 3 find (f⁻¹)'(-3)

Answer 1

f(x) = x⁵ + 2x – 3

Differentiating w.r.t. x, we get

f'(x) = 5x⁴ + 2

At y = – 3, x = 0

∴ (f⁻¹)'(-3) = `1/("f'"(0))`

= `1/(5(0)^4 + 2)`

= `1/2`