Question

Without sketching the graph of the function, find the maximum value of y = - 5x + 4 over the interval - 4 <= x <= 3. Explain how you found this value.

Answer 1

Answer:

$y_{max}=24$

Step-by-step explanation:

Given function $y=-5x+4$ is linear function. This linear function represents the straight line on the coordinate plane. The slope of this line is $-5.$ Since the slope is negative, the linear function is decreasing for all x. This means

$\text{ if } x_1 f(x_2)$

You ar geven the interval $-4\le x\le 3.$ So, the maximum value of the function is at the point x=-4 and the minimum value of the function is at the point x=3.

At x=-4,

$y=-5\cdot (-4)+4=20+4=24.$