How do you find the equation of the tangent line to the curve #y = x^4 + 9x^2 − x#, at (1, 9)?

Answer 1

#y=21x-12#

#"we require the slope m and a point on the tangent"#
#•color(white)(x)m_(color(red)"tangent")=dy/dx" at x = 1"#
#dy/dx=4x^3+18x-1#
#x=1tody/dx=4+18-1=21#
#"using "m=21" and "(x_1,y_1)=(1,9)#
#y-9=21(x-1)#
#rArry=21x-12larrcolor(red)"equation of tangent"#
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Answer 2

To find the equation of the tangent line to the curve y = x^4 + 9x^2 − x at the point (1, 9), we need to find the slope of the tangent line at that point.

To find the slope, we take the derivative of the function y = x^4 + 9x^2 − x with respect to x.

The derivative of y = x^4 + 9x^2 − x is given by dy/dx = 4x^3 + 18x - 1.

To find the slope at x = 1, we substitute x = 1 into the derivative: dy/dx = 4(1)^3 + 18(1) - 1 = 4 + 18 - 1 = 21.

Therefore, the slope of the tangent line at the point (1, 9) is 21.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values:

y - 9 = 21(x - 1).

Simplifying this equation gives the equation of the tangent line:

y = 21x - 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.

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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