If #f(x) = 3x^2 -5x#, how do you find and use it to find an equation of the tangent line at the point (2, 2)? I have no idea how to approach this.?

Answer 1

What is it you are asked to find and use?

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

(I'm assuming the "and use it to find" was redundant)

If #f(x) = 3x^2-5x#
Then the derivative (which gives the slope of the tangent) is #f'(x) =6x-5#
(using #y# in place of #f(x)# for simplicity)
The slope of the tangent at #(x_1,y_1) = (2,2)# is #m=6(2)-5 = 7# (substituting #2# for #x# in the expression for #f'(x)#
The slope-point form of an equation for the line is #(y-y_1) = m(x-x_1)#
or, in this case #(y-2) = 7(x-2)# which simplifies as #y = 7x -12#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 3

To find the equation of the tangent line at the point (2, 2) for the function f(x) = 3x^2 - 5x, you can follow these steps:

  1. Find the derivative of the function f(x) using the power rule. The derivative of 3x^2 is 6x, and the derivative of -5x is -5.

  2. Substitute the x-coordinate of the given point (2, 2) into the derivative to find the slope of the tangent line. In this case, substitute x = 2 into the derivative 6x - 5 to get the slope.

  3. Once you have the slope, use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point (2, 2) and m is the slope you found in step 2.

  4. Substitute the values of x1, y1, and m into the point-slope form equation to obtain the equation of the tangent line.

By following these steps, you can find the equation of the tangent line at the point (2, 2) for the given function f(x) = 3x^2 - 5x.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

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.

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.

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7