Calculus

Il: Read the questions comprehensively and give the correct answers. 1. Given: g(x) = -2x2 + 3. Determine the slope of the secant lines PR, PS, and PT to the curve, given the coordinates P(1, 1), R(4, -29), S(3, -15), T(1.1 , 0.58). 2. Using the value from number 1, describe what is happening to the value of the slope of the secant line from a point (x, y) as the point approaches P. 3. Estimate the slope of the tangent line at point, P. 4. Determine the derivative of g(x)=-2x2 + 3 at x = 1, using the limit definition of the derivative and the difference quotient, g'(1)=lim g(1+h)-g(1) h+0 h 5. Determine the equation of the tangent line to g(x)= -2x~ + 3 at x = 1