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f(x)=2x³+23x²+3x+5

f'(x)=6x²+46x+3

Maximum or minimum when f'(x)=0

6x²+46x+3=0

Using the Quadratic Formula: x=(-b+-squareroot(b^...

The general form for an integrand if the integral is of the form f(x^n)dx is (1/(n+1)) * x^(n+1) +c This is applied to each term in the question, remembering the constant in the integrand:

So: f(6x...

y = 4x³ To differentiate you must find dy/dx. To calculate dy/dx, look at this example using just letters from algebra: y = ax^b dy/dx = (ab)x^(b-1) As you can see, to calcu...

Draw a free body force diagram of all the forces acting on the object.

Resolve the forces parallel and perpendicular to the plane.

Use the equation ΣF=ma to solve the accele...

It is impossible to dirctly integrate sin^2(x) so we must transform it into something that can be integrated. Trigonometry can be used to do this. Recall the identity cos(2x) = cos^2(x) - sin^2(x) and cos...