Question

Determine all the points of local maxima and local minima of the following function :
f(x)=(-3/4)x⁴-8x³-(45/2)x² +105

❌NO SPAMMING❌
​

Answer 1

Answer:

ANSWER

f(x)=( 4−3 )x 4 −8x 3 −( 245 )x 2 +105f ′(x)=( 4−3 )×4x 3−8×3x 2 −(245 )×2x=−3x 3 −24x 2 −45x=−3[x 2 +8x+15]=−3[x 2 +5x+3x+15]=−3[x(x+5)+3(x 2 +5)]

=−3(x+5(x+3)nowforcriticalpoints′ (x)=0x=−5andx=−∴atx=−5isapointofminima

∴atx=−3isapointofmaxima.