Find the Tangent Given the Point (0,-4)

Problem

y=x2+3*x−4,(0,−4)

Solution

1. Identify the function ƒ(x)=x2+3*x−4 and the point ((x_1),(y_1))=(0,−4)

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

(d(x2)+3*x−4)/d(x)=2*x+3

3. Calculate the slope m by substituting the xcoordinate of the given point into the derivative.

m=2*(0)+3

m=3

4. Apply the point-slope formula y−(y_1)=m*(x−(x_1)) using the point (0,−4) and the slope m=3

y−(−4)=3*(x−0)

5. Simplify the equation into slope-intercept form.

y+4=3*x

y=3*x−4

Final Answer

y=3*x−4

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