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Kay [80]
3 years ago
12

Find a cubic function, in the form f(x)=ax^3+bx^2+cx+d, that has a local maximum value of 4 at -3 and a local minimum value of 0

at 2. f (x) = ax3 + bx2 + cx + d.
Mathematics
1 answer:
dlinn [17]3 years ago
3 0
Wea re given with <span>f(x)=ax^3+bx^2+cx+d
</span>
taking the first derivative 
<span>f′(x) = 3ax2 + 2bx + c
substituting the conditions to the original equation
</span><span>f(−3)=4=> -27a + 9b−3c+d
</span><span>f(2)=0=>8a+4b+2c+d

</span>f′(−3)=0=>27a−6b+<span>c
</span><span>f′(2)=0=>12a+4b+c

solving through the 4x4 solver
a = 8/125
b=12/125
c=-1.152
d=1.408

The equation is equal to </span>8/125 x^3 + <span>12/125 x^2 -1.152 x + 1.408.</span><span>

</span>
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