The cubic polynomial p(x) = ax^3 + bx^2 + cx + d touches the line with equation y = 9x + 2 at the point (0, 2), and has a stationary point (-1, -7). find p(x)

Polynomials are expressions that uses variables, constants and exponents.

The polynomial is:

The polynomial is given as:

At (0,2), we have:

At  (-1,-7), we have:

Substitute

Subtract 2 from both sides

Recall that:

Integrate

We have:

Integrate

The above means that:

So, we have:

Substitute 9 for c in

Add 9 to both sides

So, we have:

The line touches means that:

So, we have:

Substitute 9 for c

Recall that:

So, we have:

Substitute , and in

So, we have:

Hence, the polynomial is:

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18.75 gallons

step-by-step explanation:

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