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How do you find the slope of a tangent line to the graph of the function #f(x)=2x^2-8x+4# at (5,14)?

Answer 1

#y=12x-46#

The equation of the tangent in #color(blue)"point-slope form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))# where m represents the slope and # (x_1,y_1)" a point on the tangent"#

#color(orange)"Reminder"#

The slope of the tangent is #dy/dx# evaluated at x = 5

#rArrdy/dx=4x-8#

#x=5 : dy/dx=20-8=12=m#

Substitute m = 12 and #(x_1,y_1)=(5,14)" into the equation"#

#y-14=12(x-5)rArry-14=12x-60#

#rArry=12x-46" is the equation of the tangent"#

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Answer 2

Ezra Adams

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) = 2x^2 - 8x + 4 is f'(x) = 4x - 8.

To find the slope at the point (5,14), substitute x = 5 into the derivative: f'(5) = 4(5) - 8 = 20 - 8 = 12.

Therefore, the slope of the tangent line to the graph of f(x) = 2x^2 - 8x + 4 at (5,14) is 12.

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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.