Application of differentiation - Jamb Mathematics Past Questions and Answers

Question 11:

• JAMB 1992

a student blows a balloon and its volume increases at a rate of \(\pi\)(20 - t²)cm³S^-1 after t seconds. If the initial volume is 0 cm³, find the volume of the balloon after 2 seconds

A. 37.00\(\pi\)
B. 37.33\(\pi\)
C. 40.00\(\pi\)
D. 42.67\(\pi\)

Question 12:

• JAMB 1995

Two variables x and y are such that \(\frac{dy}{dx}\) = 4x - 3 and y = 5 when x = 2. Find y in terms of x

A. 2x² - 3x + 5
B. 2x² - 3x + 3
C. 2x² - 3x
D. 4

Question 13:

• JAMB 1997

Find the minimum value of X² - 3x + 2 for all real values of x

A. -\(\frac{1}{4}\)
B. -\(\frac{1}{2}\)
C. \(\frac{1}{4}\)
D. \(\frac{1}{2}\)

Question 14:

• JAMB 1999

Find the value of x for which the function y = x³ - x has a minimum value.

A. \(-\sqrt{3}\)
B. \(-\sqrt{\frac{3}{3}}\)
C. \(\sqrt{\frac{3}{3}}\)
D. \(\sqrt{3}\)

Question 15:

• JAMB 1999

If the minimum value of y = 1 + hx - 3x² is 13, find h.

A. 13
B. 12
C. 11
D. 10