Question

Find the derivative, if it exists, of the function at the specified point.() = ^2 − 4 + 3 at = 1

Answer 1

Find the derivate of the expression using the general procedure to find the derivative of a polynomial function. To do it, multiply the term times the exponent of the variable and raise the variable to the original exponent minus 1:

`\begin{gathered} f(x)=x^2-4x+3 \\ f^(\prime)(x)=2x^(2-1)-4x^(1-1)-0\cdot3 \\ f^(\prime)(x)=2x-4 \end{gathered}`

Now that we have the expression for the derivative of the function, evaluate it at the value of x that is in the question statement, which is 1:

`f^(\prime)(1)=2(1)-4=2-4=-2`

The derivative of the function is -2 at x=1.