1. Verify Rolle's theorem for the function (x+2)' (x-3)* in the interval [-2,3]. Plot the curve along with the secant joining the end points and the tangents at points which satisfy Rolle 's Theorem.

Q: Determine the slope of the tangent to √1-x at the point (-8, 3).

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Q: y = 3x?+1 ; (0,1)

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Q: y = √1 - 8x, (-1, 3)

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Q: The graph of  f pases through the point (1,-8) and the slope of its tangent line at  (x, f(x)) is…

A: It is given that graph of f passes through 1 , -8 and slope of the tangent at x, fx = 2x+1i.e    f'x…

Q: 4. Which graphs of ƒ may have a point of inflection? State the coordinates of each point a) ƒ''(-4)…

A: For a function f, if its second derivative f″(x) exists at x0 and x0 is an inflection point for f,…

Q: Find all the points on the graph of (x² + y²)² = x² – y² that have horizontal tangent line.

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Q: 4) Determine the equation of the tangent line to the function 2 f(x) = x at the point (3, 9).

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Q: Find the slope of the tangent line to the curve defined by 4x² + 5xy + 3yª = 98 at the point (-5,…

A: Given equation of the curve is 4x2+5xy+3y4=98.

Q: If f(x)=x²+ax+b and the slope of tangent at x= -1 is 4 and the curve passes the point (2,4) Find…

A: I have stated the used formula in the solution