given the quadratic y = (x - 4)(2x - 1). determine the interval of which the rate of change is always…
given the quadratic y = (x - 4)(2x - 1). determine the interval of which the rate of change is always positive.
Answer
Explanation:
Step1: Expand the quadratic function
[ \begin{align*} y&=(x - 4)(2x - 1)\ &=2x^{2}-x-8x + 4\ &=2x^{2}-9x + 4 \end{align*} ]
Step2: Find the derivative
The derivative of (y = 2x^{2}-9x + 4) using the power - rule ((x^n)^\prime=nx^{n - 1}) is (y^\prime=4x-9).
Step3: Set the derivative greater than 0
We want to find when (y^\prime>0), so we solve the inequality (4x-9>0). Add 9 to both sides: (4x>9). Divide both sides by 4: (x>\frac{9}{4}).
Answer:
((\frac{9}{4},\infty))