30.f(x)5ex1sin xf9(x)5ex1cos xL(x)5f(0)1f9(0)(x20)5112(x20)52x1131.The global minimum value of }12}occurs at x52.32. (a)The values of y9and y0are both negative where thegraph is decreasing and concave down, at T.(b)The value of y9is negative and the value of y0is posi-tive where the graph is decreasing and concave up, atP.33. (a)The function is increasing on the interval (0, 2].(b)The function is decreasing on the interval [23, 0).(c)The local extreme values occur only at the endpoints ofthe domain. A local maximum value of 1 occurs at x5 23, and a local maximum value of 3 occurs at x52.34.The 24th day35.36. (a)We know that fis decreasing on [0, 1] and increasingon [1, 3], the absolute minimum value occurs at x51and the absolute maximum value occurs at an endpoint.Since f(0)50,f(1)5 22, and f(3)53, the absoluteminimum value is 22 at x51 and the absolute maxi-mum value is 3 at x53.
This is the end of the preview.
access the rest of the document.