Theory question 105
DifferentiationThe gradient function of y = ax2 + bx + c is 8x + 4. If the function has a minimum value of 1, find the values of a, b and c.
Show the model answer
Model answer
dy/dx = 2ax + b = 8x + 4, so a = 4, b = 4
Minimum where 8x + 4 = 0: x = −½
y(−½) = 4(¼) + 4(−½) + c = c − 1 = 1
c = 2
Explanation
Compare coefficients, then use the minimum point where dy/dx = 0.