Para hallar los extremos hay que resolver la ecuación
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
$$\frac{d}{d x} f{\left(x \right)} = $$
primera derivada$$25^{\frac{x}{2}} \log{\left(\sqrt{25} \right)} - 5^{x} \log{\left(5 \right)} = 0$$
Resolvermos esta ecuaciónRaíces de esta ecuación
$$x_{1} = 46$$
$$x_{2} = -26$$
$$x_{3} = 58$$
$$x_{4} = -20$$
$$x_{5} = 50$$
$$x_{6} = 80$$
$$x_{7} = -100$$
$$x_{8} = 60$$
$$x_{9} = 26$$
$$x_{10} = 74$$
$$x_{11} = 72$$
$$x_{12} = -52$$
$$x_{13} = 44$$
$$x_{14} = -98$$
$$x_{15} = -46$$
$$x_{16} = -62$$
$$x_{17} = -94$$
$$x_{18} = 14$$
$$x_{19} = -2$$
$$x_{20} = 34$$
$$x_{21} = -30$$
$$x_{22} = 86$$
$$x_{23} = -88$$
$$x_{24} = 36$$
$$x_{25} = -76$$
$$x_{26} = -44$$
$$x_{27} = -70$$
$$x_{28} = -78$$
$$x_{29} = 78$$
$$x_{30} = 48$$
$$x_{31} = -38$$
$$x_{32} = -80$$
$$x_{33} = -92$$
$$x_{34} = 30$$
$$x_{35} = 16$$
$$x_{36} = 68$$
$$x_{37} = 90$$
$$x_{38} = 38$$
$$x_{39} = -56$$
$$x_{40} = -72$$
$$x_{41} = 32$$
$$x_{42} = 70$$
$$x_{43} = -58$$
$$x_{44} = 64$$
$$x_{45} = -60$$
$$x_{46} = -68$$
$$x_{47} = 8$$
$$x_{48} = 24$$
$$x_{49} = 62$$
$$x_{50} = -24$$
$$x_{51} = -6$$
$$x_{52} = -4$$
$$x_{53} = -54$$
$$x_{54} = 18$$
$$x_{55} = 0$$
$$x_{56} = 52$$
$$x_{57} = 20$$
$$x_{58} = 96$$
$$x_{59} = -64$$
$$x_{60} = 10$$
$$x_{61} = -84$$
$$x_{62} = -48$$
$$x_{63} = 54$$
$$x_{64} = -8$$
$$x_{65} = 98$$
$$x_{66} = 4$$
$$x_{67} = 82$$
$$x_{68} = -10$$
$$x_{69} = -12$$
$$x_{70} = 56$$
$$x_{71} = -66$$
$$x_{72} = -90$$
$$x_{73} = 28$$
$$x_{74} = -22$$
$$x_{75} = -28$$
$$x_{76} = -40$$
$$x_{77} = 40$$
$$x_{78} = 88$$
$$x_{79} = 94$$
$$x_{80} = 2$$
$$x_{81} = 22$$
$$x_{82} = 84$$
$$x_{83} = -16$$
$$x_{84} = -32$$
$$x_{85} = -86$$
$$x_{86} = -82$$
$$x_{87} = 92$$
$$x_{88} = -36$$
$$x_{89} = -74$$
$$x_{90} = 76$$
$$x_{91} = -18$$
$$x_{92} = 6$$
$$x_{93} = -34$$
$$x_{94} = -14$$
$$x_{95} = -96$$
$$x_{96} = 42$$
$$x_{97} = 66$$
$$x_{98} = -42$$
$$x_{99} = 12$$
$$x_{100} = 100$$
$$x_{101} = -50$$
Signos de extremos en los puntos:
(46, 0)
(-26, 0)
(58, 0)
(-20, 0)
(50, 0)
(80, 0)
(-100, 0)
(60, 0)
(26, 0)
(74, 0)
(72, 0)
(-52, 0)
(44, 0)
(-98, 0)
(-46, 0)
(-62, 0)
(-94, 0)
(14, 0)
(-2, 0)
(34, 0)
(-30, 0)
(86, 0)
(-88, 0)
(36, 0)
(-76, 0)
(-44, 0)
(-70, 0)
(-78, 0)
(78, 0)
(48, 0)
(-38, 0)
(-80, 0)
(-92, 0)
(30, 0)
(16, 0)
(68, 0)
(90, 0)
(38, 0)
(-56, 0)
(-72, 0)
(32, 0)
(70, 0)
(-58, 0)
(64, 0)
(-60, 0)
(-68, 0)
(8, 0)
(24, 0)
(62, 0)
(-24, 0)
(-6, 0)
(-4, 0)
(-54, 0)
(18, 0)
(0, 0)
(52, 0)
(20, 0)
(96, 0)
(-64, 0)
(10, 0)
(-84, 0)
(-48, 0)
(54, 0)
(-8, 0)
(98, 0)
(4, 0)
(82, 0)
(-10, 0)
(-12, 0)
(56, 0)
(-66, 0)
(-90, 0)
(28, 0)
(-22, 0)
(-28, 0)
(-40, 0)
(40, 0)
(88, 0)
(94, 0)
(2, 0)
(22, 0)
(84, 0)
(-16, 0)
(-32, 0)
(-86, 0)
(-82, 0)
(92, 0)
(-36, 0)
(-74, 0)
(76, 0)
(-18, 0)
(6, 0)
(-34, 0)
(-14, 0)
(-96, 0)
(42, 0)
(66, 0)
(-42, 0)
(12, 0)
(100, 0)
(-50, 0)
Intervalos de crecimiento y decrecimiento de la función:Hallemos los intervalos donde la función crece y decrece y también los puntos mínimos y máximos de la función, para lo cual miramos cómo se comporta la función en los extremos con desviación mínima del extremo:
La función no tiene puntos mínimos
La función no tiene puntos máximos
No cambia el valor en todo el eje numérico