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

Critical points: $x\(\approx\)-0.738$ and $x\approx 2.403$

Absolute maximum: $h\left(2.403\right)\approx 9.434$

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

Critical points: $x\approx -0.837$ and $x\approx 2.403$

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

Absolute minimum: $h\left(4\right)\approx 61.301$

Critical points: $x\(\approx\)-0.738$ and $x\approx -2.403$

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

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

Critical points: $x\(\approx\)-0.738$ and $x\approx 2.403$

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

Absolute minimum: $h\left(4\right)\approx 61.301$