Find the Tangent Given the Point (0,5)

Problem

y=x2+4*x+5,(0,5)

Solution

1. Identify the function ƒ(x)=x2+4*x+5 and the point ((x_1),(y_1))=(0,5)

2. Find the derivative of the function to determine the general slope formula.

(d(x2)+4*x+5)/d(x)=2*x+4

3. Calculate the slope m at the given point by substituting x=0 into the derivative.

m=2*(0)+4

m=4

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

y−5=4*(x−0)

5. Simplify the equation into slope-intercept form.

y−5=4*x

y=4*x+5

Final Answer

y=4*x+5

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