How do you find the equation of a line tangent to the function #y=x^2-2# at x=1?

Answer 1

#y=2x-3#

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 line"#
Now # m=dy/dx# and substituting x = 1 into the function will give us a point on the line.
#y=x^2-2rArrdy/dx=2x#
#x=1rArrdy/dx=2xx1=2=m#
#x=1rArry=(1)^2-2=-1#
substitute m = 2 and # (x_1,y_1)=(1,-1)" into the equation"#
#rArry-(-1)=2(x-1)rArry+1=2x-2#
#rArry=2x-3" is the equation"#
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Answer 2

To find the equation of a line tangent to the function y=x^2-2 at x=1, we need to find the slope of the tangent line at that point and then use the point-slope form of a linear equation.

To find the slope, we take the derivative of the function y=x^2-2 with respect to x. The derivative of x^2-2 is 2x. Evaluating this derivative at x=1, we get a slope of 2(1) = 2.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the point of tangency and m is the slope, we substitute x1=1, y1=1^2-2=-1, and m=2 into the equation.

Therefore, the equation of the line tangent to the function y=x^2-2 at x=1 is y - (-1) = 2(x - 1), which simplifies to y = 2x - 3.

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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.

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.

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