Find the Tangent Line at x=0 f(x)=4 , x=0

Problem

ƒ(x)=4,x=0

Solution

1. Identify the function and the given point. The function is a constant function ƒ(x)=4

2. Find the ycoordinate of the point of tangency by evaluating the function at x=0

ƒ(0)=4

3. Calculate the derivative of the function to find the slope of the tangent line. The derivative of a constant is zero.

d(4)/d(x)=0

4. Evaluate the derivative at x=0 to find the slope m

m=ƒ(0)′=0

5. Apply the point-slope formula y−(y_1)=m*(x−(x_1)) using the point (0,4) and the slope m=0

y−4=0*(x−0)

6. Simplify the equation to find the final form of the tangent line.

y=4

Final Answer

y=4

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