"Hello "
- Write the equation of tangent line for curv y=root of X
or y= X^(1/2)
when X=4
please help !!
Write everything you can about what makes a figure a square
What is tens equal to?
Its 10
by using :
lim (f(a+h)-f(a))/h
h->0
??
To find the equation of the tangent line to the curve y = √x (or y = x^(1/2)) at the point where x = 4, you can follow these steps:
Step 1: Find the derivative of the function with respect to x. The derivative of y = x^(1/2) can be calculated using the power rule:
dy/dx = (1/2) * x^(-1/2)
Step 2: Evaluate the derivative at x = 4 to find the slope of the tangent line. Substitute x = 4 into the derivative expression:
dy/dx = (1/2) * 4^(-1/2) = 1/4
So, the slope of the tangent line at x = 4 is 1/4.
Step 3: Find the y-coordinate of the point on the curve where x = 4. Substitute x = 4 into the original function:
y = √4 = 2
So, the point on the curve when x = 4 is (4, 2).
Step 4: Use the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) is the point on the curve and m is the slope of the tangent line. Insert the values into the equation:
y - 2 = (1/4)(x - 4)
Simplifying the equation gives:
y = (1/4)x - 1/2
Therefore, the equation of the tangent line to the curve y = √x (or y = x^(1/2)) at x = 4 is y = (1/4)x - 1/2.