Question #306114

the curve y = f(x) has a y-intercept of 3. the tangent to this curve at the point (x, y) has an x-intercept of x+2. What is the equation of this curve?


1
Expert's answer
2022-03-07T10:07:01-0500

The slope of the tangent to the curve at the point (x,y)(x, y)  is


y=x+2y'=x+2

Integrate


y=12x2+2x+Cy=\dfrac{1}{2}x^2+2x+C

The curve y=f(x)y = f(x) has a y-intercept of 3


3=0+0+C3=0+0+C

C=3C=3

The equation of this curve is

y=f(x)=12x2+2x+3y=f(x)=\dfrac{1}{2}x^2+2x+3


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