Question

Over which interval is the graph of f(x)= -x^2 +3x+ 8 increasingly

Answer 1

`x \geq (3)/(2)`

Explanation:

First, the first derivative of the function is computed to distinguish which interval is increasing.

`f'(x) = -2\cdot x + 3`

An interval is increasing only if slope is increasing as long as x increases. Then, it is quite evident that curve is increasing for:

`x \geq (3)/(2)`

Answer 2

x<1.5

Explanation:

The equation is

`f(x)=-x^2+3x+8`

Use a graphing tool to find the vertex of the parabola.When you get the vertex from the graph, you can now write the increase as ; all x-values less than the x-value of the vertex value in the graph

From the graph, the vertex is at (1.5,10.25), the parabola opens down with maximum value y=10.25

The interval of increase is x<1.5