Find the points on the curve y = x4 − 14x2 + 6 where the tangent line is horizontal.

The points on the curve are , and .

Step-by-step explanation:

Step1

For horizontal tangent, derivative of the function and equate to zero.

Given

Equation of curve is given as follows:

Step2

Calculation:

Derivate the function with respect to x and equate to zero as follows:

Now,

And,

Therefore, the values of are .

Step3

Substitute the values of in the equation as follows:

For ,

Therefore, the point is .

For ,

Therefore, the point is .

For ,

Therefore, the point is .

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.