find the slope of the tangent line to the graph of the given function at the given value of x. find the…

find the slope of the tangent line to the graph of the given function at the given value of x. find the equation of the tangent line. y = x^4 - 5x^3 + 9; x = 2\nhow would the slope of a tangent line be determined with the given information?\na. substitute values of x into the equation and solve for y. plot the resulting points to find the linear equation.\nb. substitute values of y into the equation and solve for x. plot the resulting points to find the linear equation.\nc. set the derivative equal to zero and solve for x.\nd. substitute 2 for x into the derivative of the function and evaluate.\nthe slope of the tangent line is □.

find the slope of the tangent line to the graph of the given function at the given value of x. find the equation of the tangent line. y = x^4 - 5x^3 + 9; x = 2\nhow would the slope of a tangent line be determined with the given information?\na. substitute values of x into the equation and solve for y. plot the resulting points to find the linear equation.\nb. substitute values of y into the equation and solve for x. plot the resulting points to find the linear equation.\nc. set the derivative equal to zero and solve for x.\nd. substitute 2 for x into the derivative of the function and evaluate.\nthe slope of the tangent line is □.

Answer

Explanation:

Step1: Find the derivative of the function

Using the power - rule $\frac{d}{dx}(x^n)=nx^{n - 1}$, if $y=x^{4}-5x^{3}+9$, then $y^\prime = 4x^{3}-15x^{2}$.

Step2: Evaluate the derivative at $x = 2$

Substitute $x = 2$ into $y^\prime$: $y^\prime(2)=4\times(2)^{3}-15\times(2)^{2}$ $=4\times8 - 15\times4$ $=32-60$ $=- 28$

Answer:

$-28$