Value of x (2x+43) (2x-3)

-46

Step-by-step explanation:

2x+43=2x-3

We simplify the equation to the form, which is simple to understand

2x+43=2x-3

We move all terms containing x to the left and all other terms to the right.

+2x-2x=-3-43

We simplify left and right side of the equation.

0x=-46

0=-46

The left and right sides are not equal, therefore there is no solution. This equation is invalid.

(a) Increasing in the interval (-623, 2) and (623, ∞)

f is decreasing in the interval (∞, -623) and (2, - 623).

(b) Local maximum is f = 2 .

2 local minima  f = -623.

Step-by-step explanation:

f(x) = x^4 - 50x^2 + 2

Finding the derivative:

f'(x) = 4x^3 - 100x

This = 0 at  a turning point:

4x(x^2 - 25) = 0

x = 0,  x + -5, 5.

Find the second derivative:

f"(x) = 12x^2 - 100

When x = 0 f(x) = 2

When x = 0, f"(x) is negative so the point (0, 2) is a maximum .

When x = -5, f"(x) is  positive . Also positive when x = 5.

So the 2 local minimums are (-5, (-5)^4 - 50(-5)^2 + 2) = (-5, -623) and

(5, -623).