How do you find the equation of a line tangent to the function #y=x^35x# at x=1?
#y=2x2#
Given 
#y=x^35x#
Slope of the curve at any point on the curve is given by its
first derivative
#dy/dx=3x^25#
Slope of the curve exactly at
Substitute
#dy/dx=3(1^2)5=35 = 2#
The slope of the tangent is
The tangent is passing through the point
To find the equation of the tangent , we must know the
ycoordinate at point
For this substitute
#y=1^35(1)=15=4#
Point
We know the slope of the tangent
through which it passes
#mx+c=y#
#(2)(1)+c=4#
#c=4+2=2#
Now we have Y intercept
The equation of the tangent is 
#y=mx+c#
#y=2x2#
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To find the equation of a line tangent to a function at a specific point, you can follow these steps:
 Find the derivative of the function.
 Evaluate the derivative at the given xcoordinate to find the slope of the tangent line.
 Use the pointslope form of a line, y  y₁ = m(x  x₁), where (x₁, y₁) is the given point and m is the slope, to write the equation of the tangent line.
For the function y = x^3  5x, let's find the equation of the tangent line at x = 1.

Find the derivative of the function: dy/dx = 3x^2  5

Evaluate the derivative at x = 1 to find the slope of the tangent line: m = 3(1)^2  5 = 2

Use the pointslope form with the given point (1, f(1)): y  f(1) = 2(x  1)
Now, simplify the equation to get the final form.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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