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Chapter 5: Q. 11. (page 352)

For the polynomial function fx=4x3+9x2-30x-8.

(a) Find the real zeros of f. (b) Determine the intercepts of the graph of f. (c) Use a graphing utility to approximate the local maxima and local minima. (d) Draw a complete graph of f. Be sure to label the intercepts and turning points.

Short Answer

Expert verified

(a) The real zeroes of fare -4,-14,2.

(b) The x-intercepts are -4,-14,2.

The y-intercepts are y=-8.

(c) The maxima are 2434.

The minima are -25.

(d) The graph is :

Step by step solution

01

(a) Step 2. Real zeroes of a function. 

For real zeroes of a function, fx=0

We know that

4x3+9x2-30x-8=0x-24x2+17x+4=0x-24x2+16x+x+4=0x-24xx+4+1x+4=0x-2x+44x+1=0x=2,-4,-14.

The real zeroes of a function are2,-4,-14.

02

(a) Step 3. Intercepts of a given function. 

For y-intercept, we have x=0,

y=fx=4x3+9x2-30x-8y=0+0-0-8y=-8.

For x-intercept, we have y=0,

4x3+9x2-30x-8=0x-2x+44x+1=0x=2,-4,-14.
03

(c) Step 4. Graphing Utility.

The graph is

The maximum value is 60.75 at the point x=-52.

The minimum point is -25 at the pointx=1.

04

(d) Step 5. Graphing Utility.

The graph is

05

Step 1. Given information.

The given function is

fx=4x3+9x2-30x-8.

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