Section 5
Practise questions
Question 4 Find the first-order and the second-order derivatives
a) \(f(x) = 10x + 2\)
b) \(f(x) = 80x - 2x^{2}\)
c) \(f(x) = 35 + 5x - 4x^{2} + x^{3}\)
d) \(f(x) = 90x^{2} - x^{3}\)
e) \(f(x) = (2x - 4)^{4}\)
f) \(f(x) = 2 \sqrt{x}\)
g) \(f(x) = 2q^{3} - 12q^{2} + 30q\)
h) \(f(x) = q^{3} - 9q^{2} + 45q\)
a) \({f}'(x) = 10\) \({f}''(x) = 0\)
b) \({f}'(x) = 80 - 4x\) \({f}''(x) = -4\)
c) \({f}'(x) = 5 - 8x + 3x^{2}\) \({f}''(x) = -8 + 6x\)
d) \({f}'(x) = 180x - 3x^{2}\) \({f}''(x) = 180 - 6x\)
e) \({f}'(x) = 8(2x - 4)^{3}\) \({f}''(x) = 48(2x - 4)^{2}\)
f) \({f}'(x) = \frac{1}{x^{0.5}}\) \({f}''(x) = -0.5x^{-1.5}\)
g) \({f}'(x) = 6q^{2} - 24q + 30\) \({f}''(x) = 12q - 24\)
h) \({f}'(x) = 3q^{2} - 18q + 45\) \({f}''(x) = 6q - 18\)
UWO Economics Math Resources by Mohammed Iftekher Hossain is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.