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Alternatively, having been given the derivatives at a point $a = \\var{pointQ}$, we can reconstruct the cubic function using Taylor's theorem. Since

\\[\\begin{align*}p(x) &= \\sum_{i=0}^3 \\frac{p^{(i)}(a)}{i!} (x-a)^i \\\\ &= \\frac{\\var{derivs[0]}}{0!}(\\simplify{x-{pointQ}})^0 + \\frac{\\var{derivs[1]}}{1!} (\\simplify{x-{pointQ}})^1 + \\frac{\\var{derivs[2]}}{2!} (\\simplify{x-{pointQ}})^2 + \\frac{\\var{derivs[3]}}{3!} (\\simplify{x-{pointQ}})^3 \\\\ &= \\simplify[all,!collectNumbers,!noLeadingMinus]{{derivs[0]} + {derivs[1]} (x-{pointQ}) + {derivs[2]}/2 (x-{pointQ})^2 + {derivs[3]}/6 (x-{pointQ})^3},\\end{align*}\\]

into which we can then substitute $x = \\var{pointA}$ in order to find $p(\\var{pointA}) = \\var{valueA}$.

If you expanded the brackets to find the function in its simplest form, you should have obtained

\\[p(x) = \\simplify[all,!collectNumbers,!noLeadingMinus]{{coeffs[0]} + {coeffs[1]} x + {coeffs[2]} x^2 + {coeffs[3]} x^3}.\\]

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What is $p(\\var{pointA})$?

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As you are being asked for a cubic, your function is of the form $p(x)=a x^3+b x^2+c x+ d$. You may compute the formal derivative $p'(x)$ of $p(x)$ and then evaluate it in the given points.

What is the expression of $p'(x)$?

Now you can compute the second derivative of $p(x)=a x^3+b x^2+c x+ d$.

What is $p''(x)$?

Now you can compute the third derivative of $p(x)=a x^3+b x^2+c x+ d$.

What is $p^{(3)}(x)$?

We now start computing the actual values of the coefficients of $p(x)=a x^3+b x^2+c x+ d$. Since you know $p^{(3)}(x)$ and $p^{(3)}(\\var{pointQ})$, you can compute $a$.

What is $a$?

Then you can compute $b$ from the expression of $p''(x)$.

What is $b$?

Next calculate $c$ from the value of $p'(x)$ at $\\var{pointQ}$.

What is $c$?

Finally, compute $c$ from the value of $p(x)$ at $\\var{pointQ}$.

What is $d$?

Now that you have all the coefficients of the polynomial $p(x)$, what is the value of $p(x)$ at $\\var{pointQ}$?

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I am thinking of a cubic function. Its derivatives at $a = \\var{pointQ}$ are the following:

\\[\\begin{align*} p(\\var{pointQ}) &= \\var{derivs[0]}; \\\\ p^{(1)}(\\var{pointQ}) &= \\var{derivs[1]}; \\\\ p^{(2)}(\\var{pointQ}) &= \\var{derivs[2]}; \\text{ and} \\\\ p^{(3)}(\\var{pointQ}) &= \\var{derivs[3]}. \\end{align*}\\]

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Given the derivatives of a cubic function at a point, find the value of the function at another point.

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