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