Question to test your Finding Global Extrema knowledge

Question

Find the critical points, the absolute maximum value, and the absolute minimum value of the function $h (x) = 3^{x} \sin x$ on the interval $open bracket negative 1 comma 4 close bracket$ (round to three decimal places). Also, plot the function using a graphing utility.

Accepted Answer

Critical points: $x\approx-0.738$ and $x almost equals 2.403$

Absolute maximum: $h of 2.403 almost equals 9.434$

Absolute minimum: $h(4)\approx-61.301$

Graph of the function h(x)=3^x sin x, showing critical points and behavior on the interval [-1, 4].

Answer

Critical points: $h (x) = 3^{x} \sin x$ and $x almost equals 2.403$

Absolute maximum: $h(2.403)\approx9.434$

Absolute minimum: $h of 4 almost equals 61.301$

Graph of the function h(x)=3^x sin x, showing critical points and extrema on the interval [-1, 4].

Answer

Critical points: $x\approx-0.738$ and $x almost equals 2.403$

Absolute maximum: $h (- 2.403) \approx 9.434$

Absolute minimum: $h(4)\approx-61.301$

Graph of the function h(x)=3^x*sin(x) showing critical points and extrema on the interval from -1 to 4.

Answer

Critical points: $x\approx-0.738$ and $x almost equals 2.403$

Absolute maximum: $h(2.403)\approx9.434$

Absolute minimum: $h of 4 almost equals 61.301$

Graph of the function h(x)=3^x*sin(x) showing critical points and extrema on the interval [-1, 4].

Finding Global Extrema: Study with Video Lessons, Practice Problems & Examples

Find the critical points, the absolute maximum value, and the absolute minimum value of the function h(x)=3xsin⁡xh(x)=3^{x}\sin x on the interval [−1,4][-1, 4] (round to three decimal places). Also, plot the function using a graphing utility.

Find the critical points, the absolute maximum value, and the absolute minimum value of the function $h (x) = 3^{x} \sin x$ on the interval $open bracket negative 1 comma 4 close bracket$ (round to three decimal places). Also, plot the function using a graphing utility.