How do you find the slope of a tangent line to the graph of the function #f(x)= 13 − x^2 # at (3,4)?

Answer 1

Elijah Abram

#"slope " =-6#

#" the slope (m) of the tangent to f(x) at x = a is"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(m=f'(a))color(white)(2/2)|)))#

#f(x)=13-x^2rArrf'(x)=-2x#

#rArrf'(3)=-2(3)=-6=m#

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Answer 2

Aurora Alvarado

To find the slope of a tangent line to the graph of a function at a specific point, you can use the derivative of the function. The derivative of f(x) is f'(x) = -2x. To find the slope at (3,4), substitute x = 3 into the derivative: f'(3) = -2(3) = -6. Therefore, the slope of the tangent line to the graph of f(x) = 13 - x^2 at (3,4) is -6.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.