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- Determine whether each of the following statements is true or false, and explain why. The derivative of a sum is the sum of the derivatives.If the instantaneous rate of change of f(x) with respect to x is positive when x=1, is f increasing or decreasing there ?YOUR TURN Find an equation of the curve whose tangent line has slope f(x)=3x1/2+4 and passes through the point (1,2).