What is the equation of the tangent line of f(x)=6x−x2 at x=-1?

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stefjumnmt · Accepted Answer

Explanation:We are givenf(x)=6x−x2To find the equation of the tangent line, we need to: find the slope of the tangent line, obtain a point on the line, and write the tangent line equation.To find the slope of the tangent line, we take the derivative of our function.f&#039;(x)=6-2xSubstituting our point x=-1f&#039;(-1)=6-2(-1)=6+2=8Now that we have our slope, we need to find a point on the line. We have an x-coordinate, but we need a f(x) too.f(−1)=6(−1)−(−1)2=−6−1=−7So the point on the line is (-1, -7).With a slope and a point on the line, we can solve for the equation of the line.y−yp=m(x−xp)y-(-7)=8(x-(-1))y+7=8x+8y=8x+1Hence, the tangent line equation is: f(x)=8x+1

regresavo552 · Accepted Answer

Explanation:we require the slope m and a point (x,y) on the linemtangent=f′(−1)⇒f′(x)=6−2x⇒f′(−1)=6+2=8and f(−1)=−6−1=−7⇒(−1,−7)⇒y+7=8(x+1)⇒y=8x+1← equation of tangent

What is the equation of the tangent line of f(x)=6x-x^{2}

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