How do you find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = -3 and g’(5) = 4?

Answer 1
If #g(5) = -3# then the point on the line for the required tangent is #(5,-3)#
If #g'(5) = 4# then the slope of the tangent at that point is #4#
The tangent line can be specified by the slope-point form of the equation: #(y-y_1)=m(x-x_1)# which in this case is #(y-(-3)) = 4(x-5)#
#y+3 = 4x -20#
#y = 4x -23#
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Answer 2

To find the equation of the tangent line to the graph of y = g(x) at x = 5, we can use the point-slope form of a linear equation.

The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

Given that g(5) = -3 and g’(5) = 4, we have the point (5, -3) on the tangent line and the slope of the tangent line is 4.

Using the point-slope form, the equation of the tangent line is y - (-3) = 4(x - 5).

Simplifying this equation gives y + 3 = 4x - 20.

Therefore, the equation of the tangent line to the graph of y = g(x) at x = 5 is y = 4x - 23.

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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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