Draw a graph with a positive first derivative (meaning all values are > 0) and a...

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Draw a graph with a positive first derivative (meaning all values are > 0) and a negative second derivative (all values are < 0) 2] Sketch the original function given the graph of the first and second derivatives. [Red is the first derivative, Blue is the second] 20 10 50 3] Use the power rule (and addition rule) to find the derivatives of the following functions: a) f(x)=x²-15r² + 12 b) f(x) = 3√/23 c) 1-27-1002¹.5 4 Recall that we used values really close 0, such at-00001 and .00001 to guestimate that lima-01. In this problem, we will use a tangent line approximation to further reinforce that limg-0 in(x) <= 1. a) The derivative of sin(z) is cos(z). Use this to find the tangent line of sin(z) at 0. b) Using the tangent line from part a, replace the sin(z) in limo -1 with the tangent line, and take the limit as z gots to 0. 5] Nicolas Cage is driving his Lamborghini Diablo VT to a movie premiere. His distance away from his home is given by the function D(t) = -1³ +3t. a) Use the first derivative to find how long it takes Nicolas Cage to get to the movie premiere in his Lamborghir Diablo VT. b) How fast is Nicolas Cage driving his Lamborghini Diablo VT when t = .5? When t = 1.5? c) How fast is Nicolas Cage's Lamborghini Diablo VT accelerating when t = 5? When t = 1.5? Draw a graph with a positive first derivative (meaning all values are > 0) and a negative second derivative (all values are < 0) 2] Sketch the original function given the graph of the first and second derivatives. [Red is the first derivative, Blue is the second] 20 10 50 3] Use the power rule (and addition rule) to find the derivatives of the following functions: a) f(x)=x²-15r² + 12 b) f(x) = 3√/23 c) 1-27-1002¹.5 4 Recall that we used values really close 0, such at-00001 and .00001 to guestimate that lima-01. In this problem, we will use a tangent line approximation to further reinforce that limg-0 in(x) <= 1. a) The derivative of sin(z) is cos(z). Use this to find the tangent line of sin(z) at 0. b) Using the tangent line from part a, replace the sin(z) in limo -1 with the tangent line, and take the limit as z gots to 0. 5] Nicolas Cage is driving his Lamborghini Diablo VT to a movie premiere. His distance away from his home is given by the function D(t) = -1³ +3t. a) Use the first derivative to find how long it takes Nicolas Cage to get to the movie premiere in his Lamborghir Diablo VT. b) How fast is Nicolas Cage driving his Lamborghini Diablo VT when t = .5? When t = 1.5? c) How fast is Nicolas Cage's Lamborghini Diablo VT accelerating when t = 5? When t = 1.5?

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3 Use the power rule and addition rule to find the derivatives of the following functions a fxx415x2... View the full answer