Problem+62+Marlee+and+Deborah

Using the given derivatives and second derivatives at the point where x = 3, you can figure out the shape of the function graph and therefore the relationship between time and temperature. a) f'(3) = 2, f(3) = 4 The first derivative is positive, meaning the function is increasing. The second derivative is positive, meaning the function is concave up. So the temperature would be rising quickly by more degrees each second. b) f'(3) = 2, f(3) = - 4 First derivative = positive; function is increasing. Second derivative = negative; function is concave down. The temperature would rise more slowly as time went on. c) f'(3) = - 2, f(3) = 4 First derivative = negative; function is decreasing. Second derivative = positive; function is concave up.The temperature would be falling at a slower rate with the passage of time. d) f'(3) = -2, f(3) = -4 First derivative = negative; function is decreasing. Second derivative = negative; function is concave down.The temperature would be falling quickly, getting colder by more degrees each second.



This is very good!! ms. Sweeney