Question 1122638
Express the polynomial as:
{{{ a*x^3 + b*x^2 + c*x + d }}}
The slope at any point is
{{{ a*x^2 + b*x + c }}}
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( -2, 79 )
{{{ a*(-2)^2 + b*(-2) + c = -24 }}}
{{{ 4a - b + c = -24 }}}
and
{{{ a*(-2)^3 + b*(-2)^2 +c*(-2) + d = 79 }}}
{{{ -8a + 4b - 2c + d = 79 }}}
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(1,-20)
{{{ a*1^2 + b*1 + c = -24 }}}
{{{ a + b + c = -24 }}}
and
{{{ a*1^3 + b*1^2 + c*1 + d = -20 }}}
{{{ a + b + c + d = -20 }}}
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You have 4 equations with 4 unknowns,
So solve by any means you want