Question

f(X)=x^4-62x^2+120x+9​

Answer 1

Step-by-step explanation:

The roots (zeros) are the

x

values where the graph intersects the x-axis. To find the roots (zeros), replace

y

with

0

and solve for

x

.

x

≈

−

8.69916641

,

−

0.07229949

,

2.1665023

,

6.6049636

Answer 2

Answer:

f(x) = x4 – 62x2 + 120x + 9

∴ f'(x) = 4x3 – 124x + 120 = 4(x3 – 31x + 30)

f''(x) = 12x2 – 124 = 4(3x2 – 31)

for maxima and minima,

f'(x) = 0

4(x3 – 31x + 30) = 0

So roots will be x = 5, 1, – 6

Now,

f''(5) = 176 > 0

x = 5 is point of local minima

f''(1) = – 112 < 0

x = 1 is point of local maxima

f''(– 6) = 308 > 0

x = – 6 is point of local minima

local max value = f(1) = 68

local min value = f(5) = – 316

and f(– 6) = – 1647