新高考數(shù)學(xué)一輪復(fù)習(xí) 導(dǎo)數(shù)專項重點難點突破專題25 導(dǎo)數(shù)中的三角函數(shù)問題(原卷版)

專題25導(dǎo)數(shù)中的三角函數(shù)問題1．已知函數(shù)SKIPIF1<0，SKIPIF1<0，SKIPIF1<0(1)已知SKIPIF1<0，求SKIPIF1<0的值；(2)是否存在SKIPIF1<0，使得對任意SKIPIF1<0，恒有SKIPIF1<0成立？說明理由.2．設(shè)函數(shù)SKIPIF1<0.（1）若SKIPIF1<0在SKIPIF1<0處的切線為SKIPIF1<0，求SKIPIF1<0的值；（2）當(dāng)SKIPIF1<0時，SKIPIF1<0恒成立，求SKIPIF1<0的范圍.3．設(shè)函數(shù)SKIPIF1<0．（1）若SKIPIF1<0在SKIPIF1<0上存在零點，求實數(shù)SKIPIF1<0的取值范圍；（2）證明：當(dāng)SKIPIF1<0時，SKIPIF1<0．4．已知函數(shù)SKIPIF1<0.（1）證明：當(dāng)SKIPIF1<0時，函數(shù)SKIPIF1<0有唯一的極大值；（2）當(dāng)SKIPIF1<0恒成立，求實數(shù)SKIPIF1<0的取值范圍.5．已知函數(shù)SKIPIF1<0．（1）當(dāng)a=2時，證明：SKIPIF1<0在SKIPIF1<0上單調(diào)遞減．（2）若對任意x≥0，SKIPIF1<0恒成立，求實數(shù)a的取值范圍．6．已知函數(shù)SKIPIF1<0(1)若SKIPIF1<0，求曲線SKIPIF1<0在SKIPIF1<0處的切線方程；(2)若SKIPIF1<0在SKIPIF1<0上有兩個極值點，求實數(shù)SKIPIF1<0的取值范圍.7．已知函數(shù)SKIPIF1<0(1)若SKIPIF1<0，判斷f（x）在（SKIPIF1<0，0）的單調(diào)性；(2)SKIPIF1<0在[0，SKIPIF1<0]上有且只有2個零點，求a的取值范圍.8．已知函數(shù)SKIPIF1<0，SKIPIF1<0(1)若SKIPIF1<0在SKIPIF1<0處的切線為SKIPIF1<0，求實數(shù)a的值；(2)當(dāng)SKIPIF1<0，SKIPIF1<0時，求證：SKIPIF1<09．已知函數(shù)SKIPIF1<0.(1)求SKIPIF1<0的圖象在點SKIPIF1<0處的切線方程，并證明SKIPIF1<0的圖象上除點SKIPIF1<0以外的所有點都在這條切線的上方；(2)若函數(shù)SKIPIF1<0，SKIPIF1<0，證明：SKIPIF1<0.（其中SKIPIF1<0為自然對數(shù)的底數(shù)）10．已知SKIPIF1<0（SKIPIF1<0且SKIPIF1<0），SKIPIF1<0．(1)求SKIPIF1<0在SKIPIF1<0上的最小值；(2)如果對任意的SKIPIF1<0，存在SKIPIF1<0，使得SKIPIF1<0成立，求實數(shù)a的取值范圍．11．已知函數(shù)SKIPIF1<0.(1)當(dāng)SKIPIF1<0時，SKIPIF1<0，求實數(shù)SKIPIF1<0的取值范圍；(2)證明：SKIPIF1<0.12．已知SKIPIF1<0．(1)當(dāng)SKIPIF1<0時，判斷函數(shù)SKIPIF1<0零點的個數(shù)；(2)求證：SKIPIF1<0.13．已知函數(shù)SKIPIF1<0.(1)當(dāng)SKIPIF1<0時，求SKIPIF1<0的單調(diào)區(qū)間；(2)當(dāng)SKIPIF1<0時，討論SKIPIF1<0的零點個數(shù).14．已知函數(shù)SKIPIF1<0，函數(shù)SKIPIF1<0．(1)求函數(shù)SKIPIF1<0的單調(diào)區(qū)間．(2)SKIPIF1<0時，不等式SKIPIF1<0恒成立，求實數(shù)SKIPIF1<0的取值范圍．15．已知函數(shù)SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的導(dǎo)函數(shù)．(1)若SKIPIF1<0成立，求m的取值范圍；(2)證明：函數(shù)SKIPIF1<0在SKIPIF1<0上存在唯一零點．16．函數(shù)SKIPIF1<0的圖像與直線SKIPIF1<0相切.(1)求實數(shù)a的值；(2)當(dāng)SKIPIF1<0時，SKIPIF1<0，求實數(shù)m的取值范圍.17．已知函數(shù)SKIPIF1<0，SKIPIF1<0．(1)若函數(shù)SKIPIF1<0是R上的單調(diào)遞增函數(shù)，求實數(shù)m的取值范圍；(2)若SKIPIF1<0，且對任意的SKIPIF1<0，都有SKIPIF1<0恒成立，求實數(shù)a的取值范圍．18．已知函數(shù)SKIPIF1<0(1)若SKIPIF1<0在SKIPIF1<0上單調(diào)，求參數(shù)k的取值范圍；(2)若SKIPIF1<0，SKIPIF1<0，求參數(shù)k的取值范圍．19．已知函數(shù)SKIPIF1<0．(1)討論f（x）在區(qū)間[0，SKIPIF1<0]上極值的個數(shù)；(2)當(dāng)SKIPIF1<0時，SKIPIF1<0，求實數(shù)a的取值范圍．20．設(shè)函數(shù)SKIPIF1<0.(1)若SKIPIF1<0，求曲線SKIPIF1<0的斜率為SKIPIF1<0的切線方程；(2)若SKIPIF1<0在區(qū)間SKIPIF1<0上有唯一零點，求實數(shù)SKIPIF1<0的取值范圍.21．已知函數(shù)SKIPIF1<0，SKIPIF1<0為SKIPIF1<0的導(dǎo)數(shù)．(1)求SKIPIF1<0；(2)證明：SKIPIF1<0在區(qū)間SKIPIF1<0上存在唯一零點．22．已知函數(shù)SKIPIF1<0.(1)若SKIPIF1<0，判斷函數(shù)SKIPIF1<0的單調(diào)性；(2)證明：SKIPIF1<0.23．已知函數(shù)SKIPIF1<0．(1)討論函數(shù)SKIPIF1<0的單調(diào)性；(2)當(dāng)SKIPIF1<0時，證明：SKIPIF1<0．（注SKIPIF1<0，SKIPIF1<0）24．已知函數(shù)SKIPIF1<0．(1)記函數(shù)SKIPIF1<0的導(dǎo)函數(shù)是SKIPIF1<0．證明：當(dāng)SKIPIF1<0時，SKIPIF1<0；(2)設(shè)函數(shù)SKIPIF1<0，SKIPIF1<0，其中SKIPIF1<0．若0為函數(shù)SKIPIF1<0存在非負的極小值，求a的取值范圍．25．已知函數(shù)SKIPIF1<0，SKIPIF1<0．(1)若曲線SKIPIF1<0在SKIPIF