Solve f(x)=3x^3-15x-6x^2+30text{atthepointwhere}x=3

$$f ( x ) = 3 x ^ { 3 } - 15 x - 6 x ^ { 2 } + 30 \text { at the point where } x = 3$$

Solve for f, x

$$x=3$$

$$f=4$$

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$f\times 3=3\times 3^{3}-15\times 3-6\times 3^{2}+30$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$f\times 3=3^{4}-15\times 3-6\times 3^{2}+30$$

Calculate 3 to the power of 4 and get 81.

$$f\times 3=81-15\times 3-6\times 3^{2}+30$$

Multiply -15 and 3 to get -45.

$$f\times 3=81-45-6\times 3^{2}+30$$

Subtract 45 from 81 to get 36.

$$f\times 3=36-6\times 3^{2}+30$$

Calculate 3 to the power of 2 and get 9.

$$f\times 3=36-6\times 9+30$$

Multiply -6 and 9 to get -54.

$$f\times 3=36-54+30$$

Subtract 54 from 36 to get -18.

$$f\times 3=-18+30$$

Add -18 and 30 to get 12.

$$f\times 3=12$$

Divide both sides by 3.

$$f=\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$f=4$$

The system is now solved.

$$f=4 x=3$$