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How do you find the slope of the tangent line to the graph of the equation at the point with x-coordinate for #y = sqrt(x)# at p(4,2)?

Answer 1

Isaiah Allen

You first find the derivative and then use that at #x_p=4#

#y=sqrtx=x^(1/2)->#

#y'=1/2 x^(-1/2)=1/(2*sqrtx)#

Using #x_p=4#:

#y'(4)=1/(2.sqrt4)=1/4#

And this is the slope.

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Answer 2

Charles Anctil

To find the slope of the tangent line to the graph of the equation y = sqrt(x) at the point P(4,2), we first find the derivative of the function y = sqrt(x). The derivative of y with respect to x is given by y' = (1/2) * (x)^(-1/2).

Next, we evaluate the derivative at x = 4 to find the slope of the tangent line at the point P(4,2). Substituting x = 4 into the derivative expression, we get y'(4) = (1/2) * (4)^(-1/2) = 1/4.

Therefore, the slope of the tangent line to the graph of y = sqrt(x) at the point P(4,2) is 1/4.

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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.